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A224215 Number of nonnegative solutions to x^3 + y^3 + z^3 <= n^3. 5
1, 4, 11, 30, 66, 115, 200, 302, 441, 619, 829, 1085, 1395, 1771, 2200, 2666, 3228, 3843, 4564, 5351, 6185, 7143, 8158, 9349, 10526, 11934, 13375, 14896, 16652, 18381, 20370, 22411, 24629, 26963, 29406, 32101, 34840, 37766, 40920, 44164, 47587, 51200 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

David A. Corneth, Table of n, a(n) for n = 0..1500

David A. Corneth, Pari prog

FORMULA

a(n) = [x^(n^3)] (1/(1 - x))*(Sum_{k>=0} x^(k^3))^3. - Ilya Gutkovskiy, Apr 20 2018

EXAMPLE

For n=1, the four solutions are {0,0,0}, {0,0,1}, {0,1,0} and {1,0,0}, so a(1)=4.

PROG

(Python)

for a in range(99):

n = a*a*a

k = 0

for x in range(99):

s = x*x*x

if s>n: break

for y in range(99):

sy = s + y*y*y

if sy>n: break

for z in range(99):

sz = sy + z*z*z

if sz>n: break

k+=1

print(str(k), end=', ')

(PARI) a(n) = n++; p = Pol((1/(1 - x))*sum(k=0, n, x^(k^3))^3 + O(x^(n^3))); polcoeff(p, (n-1)^3); \\ Michel Marcus, Apr 21 2018

(PARI) See PARI link \\ David A. Corneth, May 22 2018

CROSSREFS

Cf. A224214.

Sequence in context: A110579 A024829 A296290 * A308082 A099065 A296262

Adjacent sequences: A224212 A224213 A224214 * A224216 A224217 A224218

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Apr 01 2013

STATUS

approved

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Last modified January 30 19:55 EST 2023. Contains 359947 sequences. (Running on oeis4.)